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On the interaction of uni-directional and bi-directional buckling of a plate supported by an elastic foundation

Citation

Wadee, MK and Lloyd, DJB and Bassom, AP, On the interaction of uni-directional and bi-directional buckling of a plate supported by an elastic foundation, Proceedings of the Royal Society A, 472, (2188) Article 20150873. ISSN 1364-5021 (2016) [Refereed Article]

Copyright Statement

Copyright 2016 The Author(s)

DOI: doi:10.1098/rspa.2015.0873

Abstract

A thin flat rectangular plate supported on its edges and subjected to in-plane loading exhibits stable post-buckling behaviour. However, the introduction of a nonlinear (softening) elastic foundation may cause the response to become unstable. Here, the post-buckling of such a structure is investigated and several important phenomena are identified, including the transition of patterns from stripes to spots and back again. The interaction between these forms is of importance for understanding the possible post-buckling behaviours of this structural system. In addition, both periodic and some localized responses are found to exist as the dimensions of the plate are increased and this becomes relevant when the characteristic wavelengths of the buckle pattern are small compared with the size of the plate. Potential applications of the model range from macroscopic industrial manufacturing of structural elements to the understanding of micro- and nanoscale deformations in materials.

Item Details

Item Type:Refereed Article
Keywords:buckling, plates, numerical solutions, bifurcation analysis, post-buckling
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Bassom, AP (Professor Andrew Bassom)
ID Code:108239
Year Published:2016
Deposited By:Mathematics and Physics
Deposited On:2016-04-15
Last Modified:2017-11-01
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